The prenucleolus for games with communication structures

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Abstract

It is well-known that the prenucleolus on the class of TU games is characterized by singlevaluedness, covariance under strategic equivalence, anonymity, and the reduced game property. We show that the prenucleolus on the class of TU games restricted to the connected coalitions with respect to communication structures may be characterized by the same axioms and a stronger version of independence of non-connected coalitions requiring that the solution does not depend on the worth of any non-connected coalition. Similarly as in the classical case, it turns out that each of the five axioms is logically independent of the remaining axioms and that an infinite universe of potential players is necessary. Moreover, a suitable definition and characterization of a prekernel for games with communication structures is presented.
Original languageUndefined
Place of PublicationEnschede
PublisherUniversity of Twente, Department of Applied Mathematics
Number of pages15
Publication statusPublished - Dec 2011

Publication series

NameMemorandum / Department of Applied Mathematics
PublisherUniversity of Twente, Department of Applied Mathematics
No.1963
ISSN (Print)1874-4850
ISSN (Electronic)1874-4850

Keywords

  • IR-78766
  • METIS-281614
  • EWI-20929
  • Solution concept
  • TU game
  • Nucleolus
  • Communication and conference structure

Cite this

Khmelnitskaya, A. B., & Sudhölter, P. (2011). The prenucleolus for games with communication structures. (Memorandum / Department of Applied Mathematics; No. 1963). Enschede: University of Twente, Department of Applied Mathematics.
Khmelnitskaya, Anna Borisovna ; Sudhölter, Peter. / The prenucleolus for games with communication structures. Enschede : University of Twente, Department of Applied Mathematics, 2011. 15 p. (Memorandum / Department of Applied Mathematics; 1963).
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Khmelnitskaya, AB & Sudhölter, P 2011, The prenucleolus for games with communication structures. Memorandum / Department of Applied Mathematics, no. 1963, University of Twente, Department of Applied Mathematics, Enschede.

The prenucleolus for games with communication structures. / Khmelnitskaya, Anna Borisovna; Sudhölter, Peter.

Enschede : University of Twente, Department of Applied Mathematics, 2011. 15 p. (Memorandum / Department of Applied Mathematics; No. 1963).

Research output: Book/ReportReportProfessional

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N2 - It is well-known that the prenucleolus on the class of TU games is characterized by singlevaluedness, covariance under strategic equivalence, anonymity, and the reduced game property. We show that the prenucleolus on the class of TU games restricted to the connected coalitions with respect to communication structures may be characterized by the same axioms and a stronger version of independence of non-connected coalitions requiring that the solution does not depend on the worth of any non-connected coalition. Similarly as in the classical case, it turns out that each of the five axioms is logically independent of the remaining axioms and that an infinite universe of potential players is necessary. Moreover, a suitable definition and characterization of a prekernel for games with communication structures is presented.

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KW - EWI-20929

KW - Solution concept

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Khmelnitskaya AB, Sudhölter P. The prenucleolus for games with communication structures. Enschede: University of Twente, Department of Applied Mathematics, 2011. 15 p. (Memorandum / Department of Applied Mathematics; 1963).